Problem:
If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true?
All alligators are creepy crawlers.
Some ferocious creatures are creepy crawlers.
Some alligators are not creepy crawlers.
Answer Choices:
A. only
B. only
C. only
D. and only
E. None must be true
Solution:
From the conditions we can conclude that some creepy crawlers are ferocious (since some are alligators). Hence, there are some ferocious creatures that are creepy crawlers, and thus II must be true. The diagram below shows that the only conclusion that can be drawn is existence of an animal in the region with the dot. Thus, neither I nor III follows from the given conditions.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions